Method for estimating clutch engagement parameters in a strategy for clutch management in a vehicle powertrain

ABSTRACT

A method is disclosed for estimating clutch engagement characteristics of a friction clutch system in a vehicle powertrain. A dynamic model of the system is used under conditions that cause clutch slipping. Algebraic equations defining a functional relationship between clutch torque and an engagement angle have characteristic parameters that are estimated using a non-linear least squares technique. A non-linear least squares technique iteratively minimizes the difference between a measured output clutch disk speed and an output clutch disk speed from the system dynamic model for the same inputs until a small insignificant error is reached. Parameter estimates are used to compile an estimated clutch engagement characteristic.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.11/471,267, filed Jun. 20, 2006. Applicants claim the benefit of thatapplication.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention relates to a method for modifying friction clutchengagement characteristics to compensate for clutch wear.

2. Background of the Invention

In a typical powertrain system for road vehicles, such as light-dutytrucks and heavy-duty trucks, torque is delivered from the vehicleengine to the torque input side of a multiple-ratio transmission througha friction clutch that is under the control of the vehicle operator.Torque is transmitted from a torque output portion of the transmissionthrough a transmission mainshaft, a driveshaft and adifferential-and-axle assembly to vehicle traction wheels. A vehicleoperator may change the overall speed ratio of the powertrain byselectively engaging and disengaging clutch elements or brake elementsin the transmission as the transmission drive ratio is upshifted anddownshifted. To effect an upshift or a downshift, the operator typicallywill open the friction clutch by relieving a clutch apply spring forceto separate an engine driven clutch friction disk and a torque outputclutch friction disk. When torque delivery is interrupted in thisfashion, ratio changes can occur in the transmission under zero torqueconditions.

When the clutch is applied following a ratio upshift or downshift, apower flow path through the clutch is reestablished following a clutchslipping mode. In order to maintain optimum shift quality, a desiredcalibrated relationship of clutch torque and clutch engagement anglemust be maintained during the clutch engagement interval. Although acorrect functional relationship of clutch torque and clutch engagementangle can be precalibrated initially, clutch wear, which will inevitablytake place due to numerous clutch engagements and disengagements, willresult in a change in the functional relationship of clutch torque andengagement angle. Shift quality then may deteriorate and clutch controlsystem failures may occur because of excessive wear. This deteriorationof clutch performance due to wear also will affect vehicle launch from astanding start as the vehicle operator engages the clutch frictiondisks.

Currently, this clutch friction disk wear problem is dealt with byscheduling periodic time-consuming servicing of the vehicle, whichresults in an increase in overall operating costs and unproductivedown-time for the vehicle.

SUMMARY OF THE INVENTION

An objective of the invention is to provide for an automatic control forclutch engagement management that avoids the problems identified in thepreceding background discussion without a need for manual intervention.

Typically, a road vehicle, such as a truck, can be operated in one ofthree operating modes; i.e., a torque mode, a speed mode, or a combinedtorque and speed mode. For purposes of describing an embodiment of thepresent invention, it will be assumed that the vehicle is operated in aspeed mode, which essentially is similar to a well-known cruise controlapplication for automotive vehicles, wherein the vehicle driver sets aparticular speed for the vehicle to maintain. The speed mode of controlensures that the truck will maintain the set speed. The torque at thewheels for the vehicle is controlled during clutch engagements bycontrolling the engine torque delivered through the clutch to thetransmission as a function of the clutch engagement angle.

The clutch torque for a given engagement angle can be determined byusing a precalibrated functional relationship between clutch torque andengagement angle, which may be stored in the form of algebraic equationsin powertrain controller memory registers. As clutch wear occurs in aclutch system incorporating the invention, a new revised functionalrelationship of clutch torque and engagement angle is obtained in orderto maintain shift quality and to predict when excessive clutch wear hasoccurred following continuous use.

A development of a revised or current relationship between clutch torqueand engagement angle is achieved using a driveline system dynamic model.The method of the invention will estimate parameters for characteristicalgebraic functions that define a relationship of engagement angle andclutch torque and insert them in the equations in the system model. Theclutch behavior then will resemble as close as possible, followingclutch wear, the behavior of the clutch in an earlier period of theclutch operating history. A new functional relationship between clutchtorque and engagement angle with new parameters is used at periodicintervals, rather than an original functional relationship with aprecalibrated set of parameters.

Although the invention can be applied to a road vehicle, as disclosed inthis specification, it also could be used in a powertrain for otherapplications, such as tracked vehicles, tractors and mobile buildingconstruction equipment.

For purposes of this disclosure, the term “engagement angle” refers tothe angle of a clutch mechanical actuator or linkage under the controlof the vehicle operator to adjust the spacing between the clutch torqueinput friction disk and the clutch torque output friction disk duringclutch engagements and disengagements. The angle of the clutch diskmechanical actuators is a control variable used to define the algebraicequations for the system model. If the clutch is a fluid pressureactuated clutch, the variable that can be used may be the pressureapplied to a pressure operated clutch engagement and disengagementcontrol servo. The term “engagement angle,” therefore, is a generic termthat can apply to a variety of clutch actuators under the control of thevehicle operator, including electromagnetic actuators where the variablewould be voltage. Typically, clutch friction disk motion may be relatedlinearly to driver-operated foot pedal displacement. The relationship ofclutch disk motion and pedal displacement, however, need not be linear.

The control strategy of the invention makes use of a given engine inputtorque and engagement angle, which are used in solving dynamic equationsof the vehicle driveline system model to obtain a clutch output speed.The output speed is determined by the functional relationship of clutchtorque and engagement angle stored in memory registers of an electronicdigital microprocessor controller with read-only memory (ROM) in whichcontrol algorithms reside. Random access memory (RAM) stores controldata, such as engine speed and clutch speed, during repetitive controlloops. A central processor unit uses the stored data in executingalgorithms in ROM.

In estimating revised parameters for a functional relationship betweenengagement angle and clutch torque, which comprises a mathematicalconstruct, the parameters are determined by assuming torque equilibriumduring slipping of the clutch disks. The mathematical construct may, forexample, be in the form of polynomial equations. The relationshipbetween clutch torque and engagement angle is initially calibrated usingmeasured or known data.

Following clutch wear, the parameters of the functional relationship ofengagement angle and clutch torque are determined or estimated by usingdynamic equations of the driveline and “in-vehicle” measurements ofengagement angle, engine torque, engine speed and output clutch diskspeed.

The parameter estimation is done by introducing known inputs to thesystem model and integrating system dynamic equations to find outputs.The dynamic equations of the disclosed embodiments of the invention mayinclude a first derivative of a clutch speed term and a first derivativeof an engine speed term, but derivatives of other terms could beincluded as well in the dynamic equations. Thus the integral of eachderivative will yield engine speed and clutch speed, two of the outputs,as well as any other terms that are included. The other output, clutchtorque, is computed algebraically.

Initially, “guess” values of parameters of the functional relationshipof engagement angle and output clutch disk torque are used. The guessvalues are based on experience. This is followed by an optimizationmethod that computes new parameters. This optimization method minimizesthe differences between the output of the model and a measured output(i.e., engine speed and clutch speed). The final estimated values forthe parameters are used in determining the current functionalrelationship of engagement angle and clutch torque (α and T_(c1)). Thenew optimized relationship of clutch torque and engagement angle isdetermined in an iterative fashion during successive control loops ofthe microprocessor and stored in ROM memory. The optimized relationshipthen is used in the functional relationship between clutch engagementangle and clutch torque for subsequent clutch engagements.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic representation of a clutch system for a vehiclepowertrain that is operated in a so-called speed mode of control;

FIG. 2 is a schematic representation of a vehicle powertrain in whichengine torque is transmitted through a clutch to a transmission;

FIG. 3 is a plot of clutch torque versus engagement angle for a clutchin a driveline, such as that shown in FIG. 2;

FIG. 3 a is a time plot of clutch disk speed for the clutchschematically shown in FIG. 2;

FIG. 4 is a plot, generally similar to the plot of FIG. 3, whichdemonstrates that multiple sets of parameters may be identified for agiven measured data set depending upon the initial guess values chosenfor the parameters; and

FIG. 5 is a flow chart of the method steps that are used in executing analgorithm for estimating parameters for dynamic clutch engagementcharacteristics.

DETAILED DESCRIPTION OF AN EMBODIMENT OF THE INVENTION

In the schematic diagram of FIG. 2, the clutch input friction disk isshown at 10 and the clutch output friction disk is shown at 12. Disk 10is drivably connected to engine 14. The clutch output disk is drivablyconnected to a transmission mainshaft or a driveline driveshaft 16.Driveline elasticity is schematically represented by a spring constant18 (Kc), and a vibration damper constant is schematically represented byat 20 (β_(c)). During upshifts and downshifts of the transmission, orduring vehicle launch, torque delivery from the engine is interrupted asthe clutch disks 10 and 12 are opened. A dynamic model of the entiresystem can be found by applying a torque equilibrium condition atvarious nodes in the structure. The dynamic equations for the drivelineshown in FIG. 2, when the clutch is slipping in an engagement mode, areindicated as follows:

$\begin{matrix}{{\overset{.}{\omega}}_{e} = {{{- \frac{\beta_{e}}{J_{e}}}\omega_{e}} - {\frac{1}{J_{e}}T_{cl}} + {\frac{1}{J_{e}}T_{e}}}} & (1) \\{{\overset{.}{\omega}}_{c} = {{{- \frac{\beta_{c}}{J_{c}}}\omega_{c}} - {\frac{1}{J_{c}}T_{l}}\; + {\frac{1}{J_{c}}T_{cl}}}} & (2) \\{T_{cl} = {F\left( {\alpha,\alpha_{0},\alpha_{1},\alpha_{2},{\ldots \mspace{11mu} \alpha_{n}}} \right)}} & (3)\end{matrix}$

where:

ω_(e)=Engine speed, measured on the vehicle;

ω_(c)=Clutch/Mainshaft speed, measured on the vehicle;

β_(e)=Crankshaft friction coefficient;

T_(e)=Engine torque=measured on the vehicle;

T_(c1)=Torque transmitted by the clutch;

J_(e)=Engine inertia;

T₁=Load torque at wheel;

β_(c)=Mainshaft and wheel friction coefficient;

J_(c)=Inertia of the mainshaft; and

α=Angle of engagement.

For purposes of this description, the term “clutch speed” means thespeed of the clutch output disk 12.

FIG. 1 illustrates in schematic block diagram form a vehicle powertrainthat is operated in a so-called speed mode. One of the inputs to anengine controller 22 for the engine 14 is a target vehicle speed that isset by the vehicle operator. It is necessary for the engine control toreceive actual speed information in order to compare it to a targetspeed. The actual speed is measured in the usual fashion and is used asone of the inputs required to make vehicle speed adjustments if theactual vehicle speed is not equal to the target speed.

The engine control 22 generates a torque request command for the engine14 that is based on the difference between the actual vehicle speed andthe target vehicle speed. If the actual vehicle speed exceeds the targetvehicle speed, the engine controller will reduce the engine torque,which in turn reduces the vehicle speed. This type of speed control iswell-known in the industry. That torque request is delivered to a clutchcontroller 24.

In FIG. 1, the controller 24, which is labeled “clutch control,” is anelectronic microprocessor that includes memory data storage registersfor storing a relationship between clutch torque and engagement angle.This functional relationship, or map, is shown in enlarged form in FIG.1 for purposes of clarity. The clutch engagement angle is labeled “α”and the clutch torque is labeled “T_(c1).” These variables will be usedlater in this description to explain the driveline dynamic equations.

For any given clutch engagement angle α, a torque input T_(c1) for theclutch control can be determined. The shape of the plot of clutch torqueT_(c1) and engagement angle α, as seen in FIG. 1, typically is “S”shaped with clutch torque and engagement angle as variables. Theengagement angle determines the state of the clutch; i.e., open,slipping or closed. The torque output disk of the clutch is mechanicallyconnected to a multiple ratio transmission 26.

In the driveline dynamic equations indicated above, the clutch diskspeed ω_(c) is determined under the assumption that the traction wheelsare directly attached to the mainshaft. This assumption, however, couldbe modified if a propeller shaft, differential gearbox, axle shafts,synchronizer clutches and synchronizer shafts would be included in thetransmission model. That would affect the dynamics in known fashion.

When the clutch is fully engaged, the clutch speed and the engine speedare equal. They are different when the clutch slips. In the curve of theplot of clutch torque T_(c1) shown in FIGS. 1 and 3, α is used as avariable and the coefficients a_(n), when chosen correctly, will makethe plot appear typically as an “S” curve as a normalized engagementangle α varies from 0 to 1.

In the plot of FIG. 3, the clutch torque T_(c1) will be 0 when theengagement angle is 0. This represents the instant when the clutch disksbegin to close and incipient slip is about to occur. When the engagementangle α is 1.0, the clutch is closed and the value for clutch torque isequal to the lower of engine torque T_(e) and static clutch torquecapacity T_(static). The parameters α₀, a₁, a₂ . . . a_(n)(coefficients) of the functional relationship between the engagementangle α and T_(c1) determine the shape of the curve, as will beexplained subsequently. Some of the parameters following wear, forexample, are known values at all times regardless of the shape of thecurve. Other parameters, as will be explained subsequently, areestimated in view of the time history of engine torque, engine speed andclutch output disk speed.

In the procedure for estimating unknown parameters, certain values areknown for engine inertia, mainshaft inertia, torque, gear inertia, shaftstiffness, etc. This will permit the solution of the system ofdifferential algebraic equations (DAE) indicated above.

Since some of the parameter values are known, as indicated previously.The shape of the curve is determined by estimating the values ofparameters that change with clutch wear using a non-linear least squaresalgorithm, which is an optimization method.

The data used in this parameter estimation technique is based uponvalues of the engagement angle, engine torque and output clutch diskspeed. Since non-linear least squares is not a global optimizationalgorithm, multiple sets of parameters, a_(n), can be identified for thesame input data to the same parameter estimation algorithm, dependingupon the initial “guess” values of the parameters. In the exampleillustrated in FIG. 4, two different sets of identified parameters canresult in two different functional relationships of clutch torque andengagement angle. When multiple solutions are obtained, the set ofparameters corresponding to the smallest value of the objective functionmust be substituted into the functional equation for the relationship ofclutch torque and engagement angle. Those parameters would be used inthe dynamic model for the driveline to obtain a value for clutch torque“T_(c1)” for a given value of engagement angle “α”, as shown at 32 inFIG. 4, assuming that the clutch is slipping.

During parameter estimation in a system of differential algebraicequations, the procedure starts by using vehicle data, observation timesand measurements. It is the goal of the non-linear least squaresoptimization method to minimize the sum of the squares of the errorsbetween the output of the model and the measured values. The errors areerrors in clutch speed. The errors could include, however, errors inengine speed and power output shaft speed as well. In this way, thecurrent functional relationship of clutch torque and engagement angle iscomputed so as to maintain good shift quality, predict clutch wear andavoid system failures due to excessive clutch wear.

The variable under the control of the operator for controlling torqueinput to the transmission is the engagement angle. The current plot ofengagement angle and clutch torque, as developed by the parameterestimation method, will replace the original calibrated plot forengagement angle and clutch torque. As previously indicated, theoriginal calibrated relationship of clutch torque and engagement angleis obtained using measured data. Following clutch wear, the actualrelationship between clutch torque and engagement angle uses theestimated parameters of the model so that the clutch system will behaveas it did prior to the occurrence of clutch wear. The parameterestimation uses the input data, whereby engine torque and engagementangle are fed into the dynamic model of the driveline system. The modelthen is integrated to define outputs.

An initial guess value for each of the parameters to be estimated isused as a first step in an iterative optimization process. The dynamicdriveline system model is integrated, as indicated above, to get a timeevolution of ω_(e) and ω_(c). An optimization method then is used toadjust the unknown parameters so as to minimize the difference betweenthe output of the model and the measured outputs. Those computedparameters, which minimize the difference, are then used to construct anew plot of clutch torque versus engagement angle.

One possible optimization method that can be used is a method known asthe Levenberg-Marquardt non-linear least squares optimization method,although other methods, such as the Gauss-Newton method, can be used aswell. The Levenberg-Marquardt algorithm used in the presentimplementation of the method, as well as other algorithms, are describedin a publication of the Technical University of Denmark entitled“Informatics And Mathematical Modeling—Methods For Nonlinear LeastSquares Problems” by K. Madson, H. B. Neilsen and O. Tingleff, 2^(nd)Edition, published April 2004. Reference may be made to that publicationfor the purpose of supplementing the present disclosure. It isincorporated herein by reference.

In executing the Levenberg-Marquardt algorithm, the initial values forthe parameters a₁, a₂, a₃ . . . a_(n) are chosen based on a first guess.These guess values are chosen based upon experience and upon knownpre-calibrated values of these parameters for a new clutch. Thecorresponding relationship of clutch torque and engagement angle isshown in FIG. 3 at 28. This relationship is substituted in the dynamicequations of the system, and the system is integrated using known inputsof engine torque and engagement angle. The corresponding output clutchdisk speed curve is shown by a dotted line in FIG. 3 a at 39. The outputclutch disk speed that is actually measured in the vehicle correspondingto the same inputs is indicated in FIG. 3 a by a full line at 37.

Curves of the type shown in FIG. 3 sometimes are referred to as Bezierplots. Other plots that do not have an “S” shape, however, could be usedin practicing the present invention.

On the curves shown in FIG. 3 a, a set of corresponding “m” points ischosen. For purposes of this description, m=4 is chosen. The selectedfour points on the measured clutch disk speed curve are indicated atpoints 34′, 36′, 38′ and 40′, respectively. The corresponding points onthe clutch disk speed output from the model are indicated at points 34,36, 38 and 40, respectively. The clutch disk speed errors between eachset of points 34 and 34′, 36 and 36′, 38 and 38′ and 40 and 40′ then aredetermined. Each error then is squared and a function F is developed,which is the sum of the squares of the errors. Thus,

F=½(e ₁ ² +e ₂ ² +e ₃ ² +e ₄ ²).

This expression for F can be generalized as follows:

F=½ΣΔe_(z) ² where z=1 to m.

After the function F is calculated, the so-called Jacobian matrix, whichinvolves partial derivatives of function F with respect to theparameters a₁, a₂, a₃ . . . a_(n); i.e., δF/δa₁, δF/δa₂ . . . δF/δa_(n),is computed.

The Jacobian matrix is defined as:

(J(a))_(zj) =δF/δa _(j)

The next step in executing the algorithm is a computation of new valuesof a₁, a₂, a₃ . . . a_(n). This is done by first calculating the stepsize h, which is defined by the following equation:

(J ^(T) J+μI)h=J ^(T) F

where μ, is a damping parameter and I is an identity matrix. The term“h” is a vector with a size equal to the number of parameters. Followingthe calculation of step size h, the new values of parameters arecalculated. This computation can be expressed as follows:

$\begin{matrix}{\alpha_{1{({new})}} = {\alpha_{1{({old})}} + h_{1}}} \\{\alpha_{2{({new})}} = {\alpha_{2{({old})}} + h_{2}}} \\\cdots \\{\alpha_{n{({new})}} = {\alpha_{n{({old})}} + h_{n}}}\end{matrix}$

The new values of a₁, a₂, a₃ . . . a_(n) then are used to calculate anew value for the partial derivative of the function F. That new valuefor the partial derivative of the function F is compared to the oldvalue for function F. If the new value is less than the old value, thatis an indication that the correction of the plot during a given controlloop of the microprocessor is correctly adjusting the clutchcharacteristics to accommodate for wear.

The routine continues by subtracting, during each control loop, theprevious computed value for the function F from the new value for thefunction F. If the difference ε between these values is an insignificantlow value, then the optimization procedure is ended. That wouldcorrespond to an insignificant difference between measured clutch speedand clutch speed computed during any given control loop of themicroprocessor controller 24. If the value for ε is not insignificantduring any given control loop, the routine will compute a new value of μand return to the previous step where partial derivatives of thefunction with respect the parameters a₁, a₂, . . . a₃ . . . a_(n) aremade using new values for a₁, a₂, a₃ . . . a_(n). Again, these newvalues for a₁, a₂, a₃ . . . a_(n) are calculated from the dynamicequations previously identified. To prevent the microprocessor fromgetting stuck in an infinite loop, the maximum number of iterations islimited to a finite value, say niter.

FIG. 5 shows the complete algorithm in block diagram form. In FIG. 5,the driveline model is indicated at 42. The initial values forparameters are obtained, as shown at 44. These can come, for example,from operator input or from sets of values stored in ROM. Newparameters, which are intermediate computed values, are indicated at 46.The values at 46 are computed using the errors between the measuredclutch disk speed ω_(c) and outputs of the model based upon the currentvalues of the parameters. The values at 46 are now transferred, as shownat 48, to a differential algebraic equation solver 50 (DAE).

Data measurements in the vehicle are done at 52, which provides enginetorque T_(e) and an engagement angle α as an input to the equationsolver 50, as shown at 54. The outputs for the system 52 are clutchspeed and engine speed as shown at 56. These values are stored in datamemory files 58 for actual data. That actual data is transferred, asshown at 60, for use in the non-linear optimization process carried outat 62, where the partial derivatives of F with respect to parameters a₁,a₂, a₃ . . . a_(n) are computed.

At step 64, it is determined whether the partial derivative of the newfunction F minus the partial derivative of the old function F is aninsignificant low value ε. If the difference ε is not insignificant, theroutine is finished and the shape of the new characteristic curve forthe clutch then will have been defined. If the difference is greaterthan ε, the routine will supply new values of the parameters from block66 via line 46 to the differential algebraic equation solver 50. Thesteps in the algorithm are repeated until the difference between thepartial derivative of the new function F and the partial derivative ofthe old function F finally becomes less than ε.

Although an embodiment has been described, it will be apparent topersons skilled in the art that modifications may be made withoutdeparting from the scope of the invention. All such modifications andequivalents thereof are intended to be defined by the following claims.

1. A method for controlling clutch engagement of a friction clutchsystem in a vehicle powertrain, the powertrain having an engine and apower transmission, the clutch system including a clutch actuator underthe control of a vehicle operator, the actuator being movable between aclutch open position and a clutch closed position in accordance with aclutch position variable to establish and disestablish a power flow pathfrom the engine to a powertrain power output element through thetransmission, the method comprising the steps of: developing a dynamicmodel of the driveline under conditions that cause clutch slipping;determining an engine torque request in response to vehicle speedrequests by the vehicle operator; determining a target engine torque;the dynamic model and an initial functional relationship of the clutchposition variable and clutch torque defining differential algebraicequations with known parameters that determine an initial clutchengagement characteristic as the clutch position variable changesbetween an initial clutch slip state value and a clutch engaged statevalue; and computing a final estimated clutch engagement characteristicfollowing clutch wear during a clutch operating time history usingestimated parameters for the dynamic model and the functionalrelationship whereby optimal clutch engagement quality is maintained. 2.The method set forth in claim 1 including the step of minimizing in aniterative fashion an error between measured clutch speed and a computedclutch speed determined by using the dynamic model for the same inputvariables, the final clutch engagement characteristic being determinedwhen the error between the measured and the computed clutch speed isinsignificant.
 3. The method set forth in claim 2 wherein the differencebetween the measured clutch speed and a clutch speed determined by usinga set of estimated parameters is minimized iteratively with a non-linearleast squares technique until a final set of estimated parameters isobtained.
 4. The method set forth in claim 1 wherein the dynamic modeland the functional relationship define the following differentialalgebraic expressions: $\begin{matrix}{{\overset{.}{\omega}}_{e} = {{{- \frac{\beta_{e}}{J_{e}}}\omega_{e}} - {\frac{1}{J_{e}}T_{cl}} + {\frac{1}{J_{e}}T_{e}}}} & (1) \\{{\overset{.}{\omega}}_{c} = {{{- \frac{\beta_{c}}{J_{c}}}\omega_{c}} - {\frac{1}{J_{c}}T_{l}}\; + {\frac{1}{J_{c}}T_{cl}}}} & (2) \\{T_{cl} = {{a_{0}\left( {1 - \alpha} \right)}^{3} + {a_{1}3{\alpha \left( {1 - \alpha} \right)}^{2}} + {a_{2}3{\alpha^{2}\left( {1 - \alpha} \right)}} + {a_{3}\alpha^{3}}}} & (3)\end{matrix}$ where, ω_(e)=Engine speed, measured from experiment;ω_(c)=Clutch/Mainshaft speed, measured from experiment; β_(e)=Crankshaftfriction coefficient; T_(e)=Engine torque, measured from vehicle;T_(c1)=Torque transmitted by the clutch, estimated; J_(e)=Engineinertia; T₁=Load torque at wheel; β_(c)=Mainshaft and wheel frictioncoefficient; J_(c)=Inertia of the mainshaft; and α=Angle of engagement.5. The method set forth in claim 2 wherein the dynamic model and thefunctional relationship define the following differential algebraicexpressions: $\begin{matrix}{{\overset{.}{\omega}}_{e} = {{{- \frac{\beta_{e}}{J_{e}}}\omega_{e}} - {\frac{1}{J_{e}}T_{cl}} + {\frac{1}{J_{e}}T_{e}}}} & (1) \\{{\overset{.}{\omega}}_{c} = {{{- \frac{\beta_{c}}{J_{c}}}\omega_{c}} - {\frac{1}{J_{c}}T_{l}}\; + {\frac{1}{J_{c}}T_{cl}}}} & (2) \\{T_{cl} = {{a_{0}\left( {1 - \alpha} \right)}^{3} + {a_{1}3{\alpha \left( {1 - \alpha} \right)}^{2}} + {a_{2}3{\alpha^{2}\left( {1 - \alpha} \right)}} + {a_{3}\alpha^{3}}}} & (3)\end{matrix}$ where, ω_(e)=Engine speed, measured from experiment;ω_(c)=Clutch/Mainshaft speed, measured from experiment; β_(e)=Crankshaftfriction coefficient; T_(e)=Engine torque, measured from vehicle;T_(c1)=Torque transmitted by the clutch, estimated; J_(e)=Engineinertia; T₁=Load torque at wheel; β_(c)=Mainshaft and wheel frictioncoefficient; J_(c)=Inertia of the mainshaft; and α=Angle of engagement.6. The method set forth in claim 3 wherein the step of estimating afinal clutch engagement characteristic comprises using estimated valuesfor parameters for the differential algebraic equations; determiningerrors between measured clutch speed and clutch speed indicated by theestimated clutch engagement characteristic at various time samples;computing the sum of the squares of the errors to define an errorfunction; and minimizing the error function in an iterative fashionuntil it does not change significantly.
 7. The method set forth in claim5 wherein the step of minimizing the error function comprises computinga partial derivative of the error function with respect each of multipleparameters of a previously computed clutch engagement characteristic;computing a corresponding engagement characteristic using a previouslycomputed engagement characteristic and partial derivatives of the errorfunctions; computing a new error function using the new parameters; andcomparing the new error function to a previously computed error functionto determine whether the new error function is not significantly lessthan the previously computed error function.
 8. The method set forth inclaim 6 wherein the step of minimizing the error function includesrepeating the error function computation if the value of the new errorfunction is not less than the value of the previously computed errorfunction by an insignificant amount.
 9. A speed-based method forcontrolling clutch engagement characteristics for a friction clutch in apowertrain for a wheeled vehicle, the friction clutch having adisplaceable actuator element that is movable by a vehicle operatorbetween a clutch open position to a clutch closed position as a powerflow path from an engine to vehicle traction wheels is established anddisestablished, the method comprising the steps of: developing adriveline system dynamic model when the friction clutch is slipping, themodel and a functional relationship based on clutch torque anddisplacement of the actuator element defining a clutch engagementcharacteristic; determining an engine torque request in response to adifference between a measured actual vehicle speed and a predeterminedtarget vehicle speed; determining a target engine torque; the clutchengagement characteristic including a known set of parameters; andestimating a clutch engagement characteristic during a period followingclutch wear to maintain optimum clutch engagement quality.
 10. Themethod set forth in claim 9 wherein the dynamic model and the functionalrelationship comprise: $\begin{matrix}{{\overset{.}{\omega}}_{e} = {{{- \frac{\beta_{e}}{J_{e}}}\omega_{e}} - {\frac{1}{J_{e}}T_{cl}} + {\frac{1}{J_{e}}T_{e}}}} & (1) \\{{\overset{.}{\omega}}_{c} = {{{- \frac{\beta_{c}}{J_{c}}}\omega_{c}} - {\frac{1}{J_{c}}T_{l}}\; + {\frac{1}{J_{c}}T_{cl}}}} & (2) \\{T_{cl} = {{a_{0}\left( {1 - \alpha} \right)}^{3} + {a_{1}3{\alpha \left( {1 - \alpha} \right)}^{2}} + {a_{2}3{\alpha^{2}\left( {1 - \alpha} \right)}} + {a_{3}\alpha^{3}}}} & (3)\end{matrix}$ where: ω_(e)=Engine speed, measured from experiment;ω_(c)=Clutch/Mainshaft speed, measured from experiment; β_(e)=Crankshaftfriction coefficient; T_(e)=Engine torque, measured from vehicle;T_(c1)=Torque transmitted by the clutch, estimated; J_(e)=Engineinertia; T₁=Load torque at wheel; β_(c)=Mainshaft and wheel frictioncoefficient; J_(c)=Inertia of the Mainshaft; and α=Angle of engagement.11. The method set forth in claim 9 wherein the estimated clutchengagement characteristic is computed following wear of the clutch in atime period later in a clutch operating history than an initial timeperiod, the estimated clutch engagement characteristic being computed byusing a new set of parameters and a least squares error function basedon a difference between actual clutch speed values and calculated clutchspeed values for given actuator element displacements.
 12. The methodset forth in claim 10 wherein: estimating the clutch engagementcharacteristic includes computing a least squares error function forclutch speeds at multiple actuator element displacements; computingpartial derivatives of the least squares error function; computing newclutch speeds at the multiple actuator element displacements using a newset of parameters and the partial derivatives of the least squares errorfunction; comparing a least square error function using the set ofparameters previously determined to a current least squares errorfunction; and repeating the clutch engagement characteristic calculationat multiple time samples until the difference in the least squares errorfunctions is insignificant.